Question

The length of a room exceeds its breadth by 8dm; if each had been increased by 2dm, the area would have been increased by 600 square dm: find the onginal dimensions of the room. ​

Answer 1

Answer:

Step-by-step explanation:

Let the breadth of the room = 'x' cm.

Then the length of the room = x + 8 cm.

Area of the room = (x)(x + 8)

Increased by 2 cm:

⇒ Length of the room = x + 2 + 8 = x + 10 cm.

⇒ Breadth of the room = x + 2 cm.

Area is increased by 60 cm^2.

⇒ x(x + 8) + 60 = (x + 10)(x + 2)

⇒ x^2 + 8x + 60 = x^2 + 12x + 20

⇒ x^2 + 8x - x^2 - 12x = -40

⇒ -4x = -40

⇒ x = 10.

So,

Breadth = 10 m.

Then, Length = x + 8

                      = 18 m.

Therefore:

⇒ Length of the room =  18 m.

⇒ Breadth of the room = 10 m.

Answer 2

Answer :- l=18 ,b=10 and area = 180
Explanation
Let l =x
Then b= x-8
Original area is x(x-8)
After increment
l=x+2
B=x-6
Area =l*b=(X+2)(X-6) = X(x-8) +60
X^2 + -4x - 12 = x^2 -8x + 60
4x= 72
X= 18
Then
L=18 b= 10
Original area = 18*10= 180